The high-level, closed-door talks on the debt limit have left most rank-and-file Members with little say in the matter, but many lawmakers are still holding out hope that their floor speeches and press releases will have an effect on negotiations.

The problem is that the White House discussions with the top eight Congressional leaders might be too far along for them to have an effect.

Congressional leaders and President Barack Obama have been working with increasing intensity to forge a deal to raise the debt ceiling by Aug. 2 and avoid defaulting on the nation's debts. But with GOP demands that a deficit reduction package be coupled with any increase in the nation's borrowing authority, many Members see an opportunity to influence the debate by pushing deficit reduction plans of their own.

Sen. Tom Coburn (R-Okla.) said he plans to unveil a deficit reduction package Monday that would slash about $9 trillion from the deficit over 10 years.

"We are waiting on some scoring to come back ... and should have it Monday," Coburn said.

Coburn's plan comes after Senate Budget Chairman Kent Conrad (D-N.D.) officially unveiled his committee's spending blueprint Monday, which would cut$4 trillion from the deficit over 10 years. Conrad's plan includes about $800 billion in cuts to defense spending and raises more than $2 trillion in revenue, according to a GOP analysis.

Conrad believes there is time to influence the White House talks and said he gave a presentation to the president and vice president Friday.

Conrad, who has long preached deficit reduction, is also looking to build his legacy in getting his ideas in the mix. Earlier this year, he announced he would not seek re-election in 2012.

Others agree with Conrad. Sen. Chris Coons (D-Del.), who is also a member of the Budget Committee, said there is always a need for good ideas.

"It's important for folks to continue to put constructive ideas on the table because this debate is far from over," Coons said. "There is very little time left, but I think there is a real hunger among many in the Congress for clear and concrete proposals on how to solve this."

But Senate Majority Whip Dick Durbin (D-Ill.), who has been included in the White House talks, appeared to give the proposals scant chance of success. "These are all good constructive ideas and could be constructive. But I am not sure where we will end up," Durbin said.

Sens. Ron Wyden (D-Ore.) and Dan Coats (R-Ind.) also are pushing a tax reform plan as a way to boost the economy and reduce the deficit. The two asked Obama, Senate Majority Leader Harry Reid (D-Nev.) and Speaker John Boehner (R-Ohio) last week to lock in a strategy for tax reform as part of a deficit deal.

Tax reform "has a proven record of creating jobs," Wyden said Tuesday. But Wyden and Coats may be out of luck. Boehner on Saturday abandoned talk of a debt deal that would have included tax reform.

Republicans have also gotten into the act. Freshman Sen. Pat Toomey (Pa.) released his own budget in May that would balance the budget by fiscal 2020 by dramatically reducing spending and turning Medicaid into a block-grant program.

Other Senate GOP freshmen have gravitated toward the issue of the deficit as a way of burnishing their conservative bona fides. Sen. Ron Johnson (Wis.) launched a short-lived filibuster last month that slowed business on the Senate floor in order to force Congress to debate the deficit matter.

Another recent arena where lawmakers have sought to influence the debate is the Senate floor, where the chamber is considering a nonbinding measure — sponsored by Democrats — that expresses the Sense of the Senate that millionaires should share in any "sacrifice" required to reduce the deficit.

Among the amendments that have been filed to the measure is a proposal from Sen. John McCain (R-Ariz.) that would allow taxpayers to designate their taxes for deficit reduction, as well as a separate amendment that would allow for fast-track procedures for spending rescissions.

Sen. Dean Heller (R-Nev.) wants to offer an amendment that would prevent Congress from being paid until there is a budget deal.

Still, some lawmakers say it's more realistic to believe that the White House negotiations will be unaffected by the plans that have been offered.

Sen. Bob Corker (R-Tenn.) said many of the plans that have been floated are for "messaging" and designed for "public consumption."

"We would be much better off in this body if we did things under regular order," Corker said. "All these things that happen in private give the ability, candidly, for both sides to message."